semlbci: An R package for Forming Likelihood-Based Confidence Intervals for Parameter Estimates, Correlations, Indirect Effects, and Other Derived Parameters

Abstract

There are three common types of confidence interval (CI) in structural equation modeling (SEM): Wald-type CI, bootstrapping CI, and likelihood-based CI (LBCI). LBCI has the following advantages: (1) it has better coverage probabilities and Type I error rate compared to Wald-type CI when the sample size is finite; (2) it correctly tests the null hypothesis of a parameter based on likelihood ratio chi-square difference test; (3) it is less computationally intensive than bootstrapping CI; and (4) it is invariant to transformations. However, LBCI is not available in many popular SEM software packages. We developed an R package, semlbci, for forming LBCI for parameters in models fitted by lavaan, a popular open-source SEM package, such that researchers have more options in forming CIs for parameters in SEM. The package supports both unstandardized and standardized estimates, derived parameters such as indirect effect, multisample models, and the robust LBCI proposed by Falk.

Keywords:

• Confidence interval
• likelihood-based confidence interval
• robust method
• structural equation modeling

Acknowledgement

We thank Wai Chan for his valuable comments on an earlier draft of this article. Correspondence concerning this article should be addressed to Shu Fai Cheung, Department of Psychology, Faculty of Social Sciences, University of Macau, Avenida da Universidade, Taipa, Macao SAR, China, or by email ([email protected]).

Notes

1 All source and output files are available at the OSF project for this manuscript: https://osf.io/b9a2p/.

2 We thank the corresponding author for the permission to use this dataset for illustration.

3 This is not the case if the argument likelihood is set to "wishart". In the current version, semlbci() will not run on a model fitted with likelihood set to "wishart".

4 This is how Satorra's (2000) method is implemented in lavTestLRT() of lavaan (version 0.6-13).

5 In future versions of semlbci, we can use lavaan to compute a and b directly because they are exported by lavTestLRT() in the latest version of lavaan at the time of writing (0.6-13).

6 This value can be changed by users for higher precision in the search.

7 This ratio can be changed by users.

Additional information

Funding

This research was supported by the Multi-Year Research Grant [MYRG2020-00242-FSS] from the University of Macau, Macao SAR, China.